Entanglement spectra of quantum Heisenberg ladders

TL;DR

This paper investigates the entanglement spectrum of gapped two-leg quantum Heisenberg ladders, revealing a close relationship with the low-energy spectrum of edges and extending concepts from quantum Hall systems to quantum magnetism.

Contribution

It demonstrates that the entanglement spectrum reflects edge spectra in quantum Heisenberg ladders and proposes a mapping to an effective temperature, extending previous conjectures.

Findings

Entanglement spectrum mirrors the low-energy edge spectrum.

The correspondence holds for any sign of exchange coupling.

A thermodynamic mapping of the reduced density matrix is proposed.

Abstract

Bipartite entanglement measures are fantastic tools to investigate quantum phases of correlated electrons. Here, I analyze the entanglement spectrum of **gapped** two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two identical periodic chains. Comparison of various entanglement entropies proposed in the literature is given. The entanglement spectrum is shown to closely reflect the low-energy gapless spectrum of each individual edge, for any sign of the exchange coupling constants. This extends the conjecture initially drawn for Fractional Quantum Hall systems to the field of quantum magnetism, stating a direct correspondence between the low-energy entanglement spectrum of a partitioned system and the true spectrum of the "virtual edges". A mapping of the reduced density matrix to a thermodynamic density matrix is also proposed via the introduction of an effective temperature.